Abstract:
We propose a hypothesis on the detailed structure for the representation of the conformal symmetry breaking term in the basic Crewther relation generalized in the perturbation theory framework in QCD renormalized in the ¯MS¯¯¯¯¯¯¯¯MS scheme. We establish the validity of this representation in the ¯MS¯¯¯¯¯¯¯¯MS approximation. Using the variant of the generalized Crewther relation formulated here allows finding relations between specific contributions to the QCD perturbation series coefficients for the flavor nonsinglet part of the Adler function DnsADnsA for the electron–positron annihilation in hadrons and to the perturbation series coefficients for the Bjorken sum rule SBjpSBjp for the polarized deep-inelastic lepton–nucleon scattering. We find new relations between the α4sα4s coefficients of DnsADnsA. Satisfaction of one of them serves as an additional theoretical verification of the recent computer analytic calculations of the terms of order α4sα4s in the expressions for these two quantities.
Keywords:
quantum field theory, conformal symmetry breaking, perturbation theory, renormalization group, relation between characteristics of inclusive processes.
Citation:
A. L. Kataev, S. V. Mikhailov, “New perturbation theory representation of the conformal symmetry breaking effects in gauge quantum field theory models”, TMF, 170:2 (2012), 174–187; Theoret. and Math. Phys., 170:2 (2012), 139–150
\Bibitem{KatMik12}
\by A.~L.~Kataev, S.~V.~Mikhailov
\paper New perturbation theory representation of the~conformal symmetry breaking effects in gauge quantum field theory models
\jour TMF
\yr 2012
\vol 170
\issue 2
\pages 174--187
\mathnet{http://mi.mathnet.ru/tmf6757}
\crossref{https://doi.org/10.4213/tmf6757}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3168831}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2012TMP...170..139K}
\elib{https://elibrary.ru/item.asp?id=20732412}
\transl
\jour Theoret. and Math. Phys.
\yr 2012
\vol 170
\issue 2
\pages 139--150
\crossref{https://doi.org/10.1007/s11232-012-0016-7}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000301478500002}
\elib{https://elibrary.ru/item.asp?id=17979430}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84857958674}
Linking options:
https://www.mathnet.ru/eng/tmf6757
https://doi.org/10.4213/tmf6757
https://www.mathnet.ru/eng/tmf/v170/i2/p174
This publication is cited in the following 41 articles:
S. V. Mikhailov, “Adler function, Bjorken polarized sum rule: confirmation of elements of the {β}-expansion and the diagrams”, J. High Energ. Phys., 2024:10 (2024)
A. L. Kataev, V. S. Molokoedov, “A generalized Crewther relation and the V scheme: analytic results in fourth-order perturbative QCD and QED”, Theoret. and Math. Phys., 217:1 (2023), 1459–1486
A. L. Kataev, V. S. Molokoedov, “Decomposed photon anomalous dimension in QCD and the
{β}
-expanded representations for the Adler function”, Phys. Rev. D, 108:9 (2023)
A. L. Kataev, V. S. Molokoedov, “Representation of the RG-Invariant Quantities in Perturbative QCD through Powers of the Conformal Anomaly”, Phys. Part. Nuclei, 54:5 (2023), 931
I. O. Goriachuk, A. L. Kataev, V. S. Molokoedov, “The $ \overline{\mathrm{MS}} $-scheme $ {\alpha}_s^5 $ QCD contributions to the Adler function and Bjorken polarized sum rule in the Crewther-type two-fold {β}-expanded representation”, J. High Energ. Phys., 2022:5 (2022)
P. A. Baikov, S. V. Mikhailov, “The {β}-expansion for Adler function, Bjorken Sum Rule, and the Crewther-Broadhurst-Kataev relation at order O($ {\alpha}_s^4 $)”, J. High Energ. Phys., 2022:9 (2022)
K.G. Chetyrkin, “Adler function, Bjorken Sum Rule and Crewther-Broadhurst-Kataev relation with generic fermion representations at order O(αs4)”, Nuclear Physics B, 985 (2022), 115988
Akrami M., Mirjalili A., “Comparing Optimized Renormalization Schemes For Qcd Observables”, Phys. Rev. D, 101:3 (2020), 034007
Aleshin S.S. Kataev A.L. Stepanyantz K.V., “The Three-Loop Adler D-Function For N=1 Sqcd Regularized By Dimensional Reduction”, J. High Energy Phys., 2019, no. 3, 196
Kim V.T., “Qcd Asymptotics At Collider Energies”, Phys. Part. Nuclei Lett., 16:5 (2019), 414–420
Wu X.-G., Shen J.-M., Du B.-L., Huang X.-D., Wang Sh.-Q., Brodsky S.J., “The Qcd Renormalization Group Equation and the Elimination of Fixed-Order Scheme-and-Scale Ambiguities Using the Principle of Maximum Conformality”, Prog. Part. Nucl. Phys., 108 (2019), UNSP 103706
A. V. Garkusha, A. L. Kataev, V. S. Molokoedov, “Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the β-factorization property?”, J. High Energ. Phys., 2018:2 (2018)
J.-M. Shen, X.-G. Wu, Ya. Ma, S. J. Brodsky, “The generalized scheme-independent Crewther relation in QCD”, Phys. Lett. B, 770 (2017), 494–499
P. Banerjee, P. K. Dhani, M. Mahakhud, V. Ravindran, S. Seth, “Finite remainders of the Konishi at two loops in $\mathcal{N}=4$ SYM”, J. High Energy Phys., 2017, no. 5, 085
S. V. Mikhailov, “On a realization of $\{\beta\}$-expansion in QCD”, J. High Energy Phys., 2017, no. 4, 169
M. R. Khellat, A. Mirjalili, “Deviation pattern approach for optimizing perturbative terms of QCD renormalization group invariant observables”, XXIII International Baldin Seminar on High Energy Physics Problems Relativistic Nuclear Physics and Quantum Chromodynamics (Baldin ISHEPP XXIII), EPJ Web Conf., 138, eds. S. Bondarenko, V. Burov, A. Malakhov, EDP Sciences, 2017, UNSP 02004
A. G. Grozin, J. M. Henn, G. P. Korchemsky, P. Marquard, “The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions”, J. High Energy Phys., 2016, no. 1, 140
A. L. Kataev, S. V. Mikhailov, “The $\{\beta\}$-expansion formalism in perturbative QCD and its extension”, J. High Energy Phys., 2016, no. 11, 079
A. Deur, S. J. Brodsky, G. F. de Teramond, “The QCD running coupling”, Prog. Part. Nucl. Phys., 90 (2016), 1–74
Citation in format AMSBIB
Contact us: